共查询到20条相似文献,搜索用时 30 毫秒
1.
Yong Kong 《Journal of Difference Equations and Applications》2013,19(15):1265-1271
The Goulden–Jackson cluster method is a powerful method to find generating functions of pattern occurrences in random sequences [1]. The method is clearly explained, extended and implemented by Noonan and Zeilberger [2]. In this paper, we elaborate on one of the several extensions in [2], namely the extension from symmetrical Bernoulli sequences where the occurrences of each symbol have equal probability, to asymmetrical Bernoulli sequences with different probabilities of symbol generations. An explicit formula is derived for the extension, which is implicitly embedded in the treatment of [2]. The extended result is then compared with the method of Régnier–Szpankowski [3], a method which was developed independently to tackle the same problem. By manipulating some matrix inversions, we show that the Régnier–Szpankowski method can be simplified to the extended Goulden–Jackson method. 相似文献
2.
Bangteng Xu 《代数通讯》2017,45(12):5202-5211
Commutative standard table algebras with exactly one multiplicity not equal to 1 are characterized by the wreath product of some special table algebras in [1]. A natural and much more general question is the characterization of standard table algebras (not necessarily commutative) with exactly one irreducible character whose degree and multiplicity are not equal and the degree is 1. We will give a characterization of such table algebras, including the main result of [1] as a special case. Applications to association schemes are also discussed. 相似文献
3.
Be’eri Greenfeld 《代数通讯》2017,45(11):4783-4784
We construct a ring which admits a 2-generated, faithful torsion module but lacks a cyclic faithful torsion module. This answers a question by Oman and Schwiebert [1, 2]. 相似文献
4.
Candace Walkington Anthony Petrosino Milan Sherman 《Mathematical Thinking and Learning》2013,15(2):89-120
Context personalization refers to matching instruction to students' out-of-school interests and experiences. Belief in the benefits of matching instruction to interests is widely held in the culture of schooling; however, little research has empirically examined how interest impacts performance and learning in secondary mathematics. Here we investigate these issues with a series of problem-solving sessions where 24 Algebra I students were presented with story problems on linear functions, some of which were personalized to their interests. Our analyses focus on performance, strategy use, and mistake patterns. Results suggest that personalization supported situational reasoning (Nathan, Kintsch, & Young, 1992) about the actions and relationships in the scenario, improving performance for weaker students and on harder problems. However, personalized scenarios seemed to act as a distraction when stronger students in the sample worked on easier problems. Thus context personalization may have the potential to provide assistance and support performance as students learn new concepts. 相似文献
5.
6.
《偏微分方程通讯》2013,38(11-12):2311-2331
ABSTRACT We study here an asymptotic limit of the Schrödinger–Poisson system. We prove that the current converges toward a dissipative solution of the Euler equations when we consider a semi-classical quasi-neutral limit. The proof involves the modulated energy introduced by Brenier in Ref. [2]. 相似文献
7.
《代数通讯》2013,41(10):4621-4627
ABSTRACT In this note we show that the hermitian level of a quaternion division algebra with involution of second kind, is always a power of 2, when it is finite. This result holds for a field with trivial or non-trivial involution, and quaternion division algebras with involution of first kind [6], [5], [9]. 相似文献
8.
《Optimization》2012,61(3):675-686
AbstractIn this paper, we characterize two power indices introduced in [1] using two different modifications of the monotonicity property first stated by [2]. The sets of properties are easily comparable among them and with previous characterizations of other power indices. 相似文献
9.
《代数通讯》2013,41(10):4945-4963
ABSTRACT We give another proof of Harrison's decomposition result,[2] Prop. 2.3 for higher degree forms over a noetherian ring, exploiting an earlier introduction of the centre. We generalise to higher degree forms over a noetherian scheme: we extend the notion of centre; we prove a decomposition result; we extend Harrison's result,[2] Prop. 4.3 on the behaviour of the centre under a flat base extension; and we improve his result,[2] Prop. 4.2, giving conditions on the base scheme under which the centre of the tensor product of two higher degree forms is isomorphic to the tensor product of their centres. 相似文献
10.
The pioneering work of Brezis-Merle [7], Li-Shafrir [27], Li [26], and Bartolucci-Tarantello [3] showed that any sequence of blow-up solutions for (singular) mean field equations of Liouville type must exhibit a “mass concentration” property. A typical situation of blowup occurs when we let the singular (vortex) points involved in the equation (see (1.1) below) collapse together. However in this case, Lin-Tarantello in [30] pointed out that the phenomenon: “bubbling implies mass concentration” might not occur and new scenarios open for investigation. In this paper, we present two explicit examples which illustrate (with mathematical rigor) how a “nonconcentration” situation does happen and its new features. Among other facts, we show that in certain situations, the collapsing rate of the singularities can be used as blow-up parameter to describe the bubbling properties of the solution-sequence. In this way, we are able to establish accurate estimates around the blow-up points which we hope to use toward a degree counting formula for the shadow system (1.34) below. 相似文献
11.
《Optimization》2012,61(6):777-793
In this article, we consider a bilevel vector optimization problem where objective and constraints are set valued maps. Our approach consists of using a support function [1–3,14,15,32] together with the convex separation principle for the study of necessary optimality conditions for D.C. bilevel set-valued optimization problems. We give optimality conditions in terms of the strong subdifferential of a cone-convex set-valued mapping introduced by Baier and Jahn 6 and the weak subdifferential of a cone-convex set-valued mapping of Sawaragi and Tanino 28. The bilevel set-valued problem is transformed into a one level set-valued optimization problem using a transformation originated by Ye and Zhu 34. An example illustrating the usefulness of our result is also given. 相似文献
12.
A. R. Nasr-Isfahani 《代数通讯》2017,45(1):443-445
In this article, we show that there exists an SCN ring R such that the polynomial ring R[x] is not SCN. This answers a question posed by T. K. Kwak et al. in [2]. 相似文献
13.
A ring is called clean if every element is a sum of a unit and an idempotent, while a ring is said to be weakly clean if every element is either a sum or a difference of a unit and an idempotent. Commutative weakly clean rings were first discussed by Anderson and Camillo [2] and were extensively investigated by Ahn and Anderson [1], motivated by the work on clean rings. In this paper, weakly clean rings are further discussed with an emphasis on their relations with clean rings. This work shows new interesting connections between weakly clean rings and clean rings. 相似文献
14.
We study the long time behavior of solutions of the Cauchy problem for semilinear parabolic equations with the Ornstein–Uhlenbeck operator in ? N . The long time behavior in the main results is stated with help of the corresponding to ergodic problem, which complements, in the case of unbounded domains, the recent developments on long time behaviors of solutions of (viscous) Hamilton–Jacobi equations due to Namah (1996), Namah and Roquejoffre (1999), Roquejoffre (1998), Fathi (1998), Barles and Souganidis (2000 2001). We also establish existence and uniqueness results for solutions of the Cauchy problem and ergodic problem for semilinear parabolic equations with the Ornstein–Uhlenbeck operator. 相似文献
15.
《代数通讯》2013,41(6):3037-3043
ABSTRACT In his recent work, [1] and [2], on the pure semisimplicity conjecture Simson raised two problems about the structure of the direct sum decomposition of the direct product modulo the direct sum of indecomposable preinjective modules over right pure semisimple hereditary rings. The main goal of this paper is the proof of a theorem that resolves one of these problems and provides a partial answer to the other. 相似文献
16.
Héctor Suárez 《代数通讯》2017,45(10):4569-4580
Pre-Koszul and Koszul algebras were defined by Priddy [15]. There exist some relations between these algebras and the skew PBW extensions defined in [8]. In [24] we gave conditions to guarantee that skew PBW extensions over fields it turns out homogeneous pre-Koszul or Koszul algebra. In this paper we complement these results defining graded skew PBW extensions and showing that if R is a finite presented Koszul 𝕂-algebra then every graded skew PBW extension of R is Koszul. 相似文献
17.
Viktoriya Ozornova 《代数通讯》2017,45(4):1760-1784
A recent theorem of Dobrinskaya [20] states that the K(π,1)-conjecture holds for an Artin group G if and only if the canonical map BM→BG is a homotopy equivalence, where M denotes the Artin monoid associated to G. The aim of this paper is to give an alternative proof by means of discrete Morse theory and abstract homotopy theory. Moreover, we exhibit a new model for the classifying space of an Artin monoid, in the spirit of [13], and a small chain complex for computing its monoid homology, similar to the one of [44]. 相似文献
18.
Let 𝒜 be an abelian category. A subcategory 𝒳 of 𝒜 is called coresolving if 𝒳 is closed under extensions and cokernels of monomorphisms and contains all injective objects of 𝒜. In this paper, we introduce and study Gorenstein coresolving categories, which unify the following notions: Gorenstein injective modules [8], Gorenstein FP-injective modules [20], Gorenstein AC-injective modules [3], and so on. Then we define a resolution dimension relative to the Gorenstein coresolving category 𝒢?𝒳(𝒜). We investigate the properties of the homological dimension and unify some important properties possessed by some known homological dimensions. In addition, we study stability of the Gorenstein coresolving category 𝒢?𝒳(𝒜) and apply the obtained properties to special subcategories and in particular to module categories. 相似文献
19.
《偏微分方程通讯》2013,38(3):283-304
ABSTRACT In this paper, we study the Cauchy problem for a pressureless type system. The Riemann solutions only include two elementary waves, delta waves and contact discontinuity. The existence of an entropy solution is established by studying the interaction of the elementary waves and the generalized characteristics introduced in Dafermos (1977). 相似文献
20.
《偏微分方程通讯》2013,38(9-10):1685-1704
Abstract The purpose of this article is to prove a sharp bound on the number of resonances for the Laplacian on conformally compact manifolds with constant negative curvature near infinity, thus improving the polynomial bound of Guillopé and Zworki (Guillopé, L., Zworski, M. ([1995b]). Polynomial bound on the number of resonances for some complete spaces of constant negative curvature near infinity. Asympt. Anal. 11:1–22). 相似文献